[en] We derived an original expression for the partial cross sections for radiative recombination (RR) of highly charged bare ions in the nonrelativistic electric-dipole approach. Three sets of cross sections for RR to individual magnetic sublevels of the excited levels of various recombined H-like ions were computed: the first two in the electric-dipole approximation with the nonrelativistic and relativistic electron wavefunctions and the third one in the exact relativistic method including all multipole orders of the radiation field. (paper)